Gravity will usually cause the padding to shift.

This is quite possible. Some mattresses are more rigid and could take standing up longer than others. If the mattress was bent in a standing position you could imagine the spring system taking on a contorted posture permanently. No sure about the previous comment but it does stand to reason that things could shift in 2 years. My biggest concern would be the change in shape of the mattress, as I would doubt the mattress would be standing in perfect up and down position.

Perhaps if it was perfectly balanced on it's side, there may not be any issue. But foam layers are glued together and after a long period of time, as Peter said, gravity can take it's toll and the adhesive's no longer hold the layers together and will bunch/fold. Depending on the thickness and coil system, it may not stand well on it's side and lean funny. If it was left for a significant period of time in an odd shape, it will likely maintain that shape when laid on the floor. In the end, that is the test to try. If you lay it flat on the floor and it looks or appears fine, it could be alright. If it doesn't lay flat or if it looks funny, it could have been damaged in the 2 years it was on it's side.

If it is a foam encased mattress, the foam on the edge has most likely compressed significantly. The shifting of the foam in the comfort layer of the mattress is less common but still possible. According to most manufacturers, the proper support for a mattress is laying on a hard flat surface. Storing a mattress on its side is not proper support leading them to claim it has been misused. Either way, it will take some time after placing the mattress down for the materials to realign and retain their original shape. Tip for the future: when storing mattresses long term, lay them completely flat on a flat surface. This will prevent abnormal compression & shifting. Good luck!